class 12

Math

Calculus

Differential Equations

Consider the family of all circles whose centers lie on the straight line `y=x`. If this family of circles is represented by the differential equation `P y^(primeprime)+Q y^(prime)+1=0,`where `P ,Q`are functions of `x , y`and `y^(prime)(h e r ey^(prime)=(dy)/(dx),y^=(d^2y)/(dx^2)),`then which of the following statements is (are) true?(a)`P=y+x`(b)`P=y-x`(c)`P+Q=1-x+y+y^(prime)+(y^(prime))^2`(d)`P-Q=x+y-y^(prime)-(y^(prime))^2`